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The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be and , then tan and tan are

Options

  1. A5 +1 2 and 5 -1 2
  2. B5 +1 2 and 5 -1 2
  3. C5 and 1 5
  4. D5 2 and 2 5

Correct answer

B. 5 +1 2 and 5 -1 2

Step-by-step solution

Let A B C be a right angled triangle at B . Let A and C be and Since, sides are in GP so sides are a, ar, ar ² array lr Now, & array r A C²=A B²+B C² (a r² )²=a²+(a r)² array a² r⁴=a²+a² r² r⁴-r²-1=0 r²= 1+ 5 2 r= 5 +1 2 array = B C A B = a r a r= 5 +1 2 aligned and &= A B B C = a a r = 1 r &= 1 5 +1 2 = 5 -1 2 aligned

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